Finite Group Databasebeta

← C113×#18885 #43286905

Subgroups — C113×#18885 #43286905

Order 28928.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3503C211yesmaximal, characteristic
2C113×#3249C211yesmaximal, characteristic, complemented
3C113×#3230C211yesmaximal, characteristic, complemented
4C113×#3076C211yesmaximal, characteristic
5C113×#1649C212yesmaximal, complemented
6C113×#1648C212yesmaximal, complemented
7C113×#1637C212yesmaximal, complemented
8C113×#1636C212yesmaximal, complemented
9C2×#332×C113C211yesmaximal, characteristic, complemented
10C113×#1481C211yesmaximal, characteristic, complemented
11C113×#1477C211yesmaximal, characteristic
12Q82×C113—21no—
13#557×C113C2212yes—
14#554×C113—21no—
15#554×C113—22no—
16D4×Q8×C113—22no—
17D4×Q8×C113C2212yes—
18#544×C113—22no—
19#544×C113—21no—
20#533×C113—21no—
21#533×C113C2211yescharacteristic
22#533×C113C2211yescharacteristic
23C2×C4⋊Q8×C113—21no—
24C2×C4⋊Q8×C113C2211yescharacteristic
25#520×C113—21no—
26C4×#41×C113C2211yescharacteristic
27#500×C113C2212yes—
28#487×C113C2212yes—
29#484×C113—22no—
30#479×C113—21no—
31#478×C113—21no—
32#477×C113—22no—
33#477×C113—21no—
34#477×C113C2211yescharacteristic
35#477×C113C2212yes—
36#476×C113C2211yescharacteristic
37#475×C113C2211yescharacteristic
38#474×C113C2211yescharacteristic
39#467×C113—22no—
40#462×C113—21no—
41#462×C113C2212yes—
42#431×C113C2211yescharacteristic
43#427×C113—21no—
44C2×C4⋊C8×C113C2211yescharacteristic
45C2×C4⋊C8×C113C2211yescharacteristic
46#416×C113—21no—
47#332×C113C2212yes—
48#332×C113C2212yes—
49Q8⋊C8×C113C2212yes—
50Q8⋊C8×C113C2212yes—
51Q8⋊C8×C113C2212yes—
52D4⋊C8×C113C2212yes—
53C2×#41×C113D411yescharacteristic
54C22×Q8×C113—22no—
55C22×Q8×C113—21no—
56C2×Q16×C113—22no—
57C22×C8×C113—21no—
58C22×C8×C113—21no—
59C4⋊Q8×C113—22no—
60C4⋊Q8×C113—22no—
61C4⋊Q8×C113—24no—
62C4⋊Q8×C113—22no—
63C4⋊Q8×C113—22no—
64C4⋊Q8×C113—21no—
65C4⋊Q8×C113—21no—
66C4⋊Q8×C113D411yescharacteristic
67C4⋊Q8×C113D412yes—
68C4⋊Q8×C113D411yescharacteristic
69C4⋊Q8×C113C2311yescharacteristic
70C4⋊Q8×C113C2311yescharacteristic
71C4⋊Q8×C113C2312yes—
72#125×C113—22no—
73#125×C113—24no—
74#125×C113—22no—
75#125×C113—21no—
76#125×C113—21no—
77C22⋊Q8×C113—22no—
78C22⋊Q8×C113—24no—
79C22⋊Q8×C113—24no—
80C22⋊Q8×C113—21no—
81C22⋊Q8×C113—22no—
82C22⋊Q8×C113—24no—
83C22⋊Q8×C113—21no—
84C22⋊Q8×C113—21no—
85C22⋊Q8×C113D412yes—
86C4×Q8×C113—22no—
87C4×Q8×C113—22no—
88C4×Q8×C113—22no—
89C4×Q8×C113—21no—
90C4×Q8×C113—21no—
91C4×Q8×C113—21no—
92C4×Q8×C113D411yescharacteristic
93C4×Q8×C113C2311yescharacteristic
94C4×Q8×C113C2312yes—
95C4×D4×C113—24no—
96C4×D4×C113—22no—
97C4×D4×C113—21no—
98C4×D4×C113—21no—
99C4×D4×C113D411yescharacteristic
100C4×D4×C113C2311yescharacteristic
101#117×C113—22no—
102#117×C113—21no—
103#117×C113—21no—
104#117×C113—21no—
105#117×C113D411yescharacteristic
106C2×C4⋊C4×C113—22no—
107C2×C4⋊C4×C113—22no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113D412yes—
110C2×C42×C113—21no—
111C2×C42×C113C2311yescharacteristic
112#107×C113—21no—
113#107×C113—21no—
114#107×C113—22no—
115#107×C113—24no—
116#106×C113—21no—
117#106×C113—21no—
118C4⋊C8×C113—21no—
119C4⋊C8×C113—21no—
120C4⋊C8×C113—21no—
121C4⋊C8×C113C2312yes—
122C4⋊C8×C113C2311yescharacteristic
123C4⋊C8×C113C2311yescharacteristic
124#103×C113—21no—
125#103×C113—21no—
126#103×C113—22no—
127#103×C113—22no—
128#103×C113—24no—
129#102×C113—21no—
130#102×C113—21no—
131C22⋊C8×C113—21no—
132C4×C8×C113C2312yes—
133#41×C113—22no—
134#41×C113Q1614yescomplemented
135C2×Q8×C113—24no—
136C2×Q8×C113—21no—
137C2×Q8×C113—22no—
138C2×Q8×C113—22no—
139C2×Q8×C113—21no—
140C2×Q8×C113—21no—
141C2×Q8×C113—81no—
142C2×Q8×C113—81no—
143C2×Q8×C113—82no—
144C2×Q8×C113—82no—
145C2×Q8×C113C2×D412yes—
146C2×Q8×C113C2×D411yescharacteristic
147C2×D4×C113—21no—
148C2×D4×C113C2×D411yescharacteristic
149C22×C4×C113—21no—
150C22×C4×C113—24no—
151C22×C4×C113—22no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113C2×D411yescharacteristic
155C22×C4×C113C2×D411yescharacteristic
156C22×C4×C113C2×D411yescharacteristic
157Q16×C113—82no—
158C2×C8×C113—22no—
159C2×C8×C113—21no—
160C2×C8×C113—21no—
161C2×C8×C113—22no—
162C2×C8×C113—42no—
163C2×C8×C113—81no—
164C4⋊C4×C113—24no—
165C4⋊C4×C113—24no—
166C4⋊C4×C113—24no—
167C4⋊C4×C113—24no—
168C4⋊C4×C113—21no—
169C4⋊C4×C113—22no—
170C4⋊C4×C113—21no—
171C4⋊C4×C113—22no—
172C4⋊C4×C113—21no—
173C4⋊C4×C113—21no—
174C4⋊C4×C113—22no—
175C4⋊C4×C113—22no—
176C4⋊C4×C113—21no—
177C4⋊C4×C113—22no—
178C4⋊C4×C113—21no—
179C4⋊C4×C113—21no—
180C4⋊C4×C113—21no—
181C4⋊C4×C113—21no—
182C4⋊C4×C113—41no—
183C4⋊C4×C113—41no—
184C4⋊C4×C113C2×D414yes—
185C4⋊C4×C113C2×D412yes—
186C4⋊C4×C113C2×D411yescharacteristic
187C4⋊C4×C113C2×D411yescharacteristic
188C22⋊C4×C113—24no—
189C22⋊C4×C113—22no—
190C22⋊C4×C113—21no—
191C22⋊C4×C113—21no—
192C22⋊C4×C113—21no—
193C22⋊C4×C113—41no—
194C42×C113—24no—
195C42×C113—21no—
196C42×C113—21no—
197C42×C113—21no—
198C42×C113—22no—
199C42×C113—41no—
200C42×C113C2×D411yescharacteristic
201C42×C113C2×D411yescharacteristic
202C42×C113C2×D411yescharacteristic
203C42×C113C2411yescharacteristic
204C23×C113—21no—
205C23×C113#12011yescharacteristic
206Q8×C113—21no—
207Q8×C113—22no—
208Q8×C113—22no—
209Q8×C113—42no—
210Q8×C113—42no—
211Q8×C113—42no—
212Q8×C113—42no—
213Q8×C113—41no—
214Q8×C113—41no—
215Q8×C113—82no—
216Q8×C113—84no—
217Q8×C113C2×Q1612yes—
218D4×C113—24no—
219D4×C113—21no—
220D4×C113C2×Q1612yes—
221C2×C4×C113—21no—
222C2×C4×C113—21no—
223C2×C4×C113—21no—
224C2×C4×C113—24no—
225C2×C4×C113—22no—
226C2×C4×C113—21no—
227C2×C4×C113—21no—
228C2×C4×C113—22no—
229C2×C4×C113—24no—
230C2×C4×C113—41no—
231C2×C4×C113—42no—
232C2×C4×C113—41no—
233C2×C4×C113—41no—
234C2×C4×C113—41no—
235C2×C4×C113—41no—
236C2×C4×C113—82no—
237C2×C4×C113—84no—
238C2×C4×C113#12011yescharacteristic
239C2×C4×C113#12011yescharacteristic
240C2×C4×C113#12011yescharacteristic
241C2×C4×C113C2×Q1612yes—
242C2×C4×C113#13712yes—
243C2×C4×C113C22×D411yescharacteristic
244C2×C4×C113C22×D411yescharacteristic
245C2×C4×C113C22×D411yescharacteristic
246C8×C113—42no—
247C8×C113—41no—
248C8×C113—41no—
249C8×C113—42no—
250C22×C113—21no—
251C22×C113—21no—
252C22×C113—22no—
253C22×C113—41no—
254C22×C113—41no—
255C22×C113#45112yes—
256C22×C113C2×#12011yescharacteristic
257C4×C113—22no—
258C4×C113—21no—
259C4×C113—21no—
260C4×C113—21no—
261C4×C113—41no—
262C4×C113—42no—
263C4×C113—44no—
264C4×C113—41no—
265C4×C113—42no—
266C4×C113—81no—
267C4×C113—81no—
268C4×C113#45112yes—
269C4×C113C22×Q1611yescharacteristic
270C4×C113C2×#13711yescharacteristic
271C4×C113#57611yescharacteristic
272C4×C113#57711yescharacteristic
273#18885C11311yesmaximal, characteristic, direct product factor, Sylow
274C2×C113—22no—
275C2×C113—42no—
276C2×C113C2×#45111yescharacteristic
277C2×C113#301211yescharacteristic
278C2×C113#302011yescharacteristic
279#3503C2×C11311yescharacteristic
280#3249C2×C11311yescharacteristic, complemented
281#3230C2×C11311yescharacteristic, complemented
282#3076C2×C11311yescharacteristic
283#1649C2×C11312yescomplemented
284#1648C2×C11312yescomplemented
285#1637C2×C11312yescomplemented
286#1636C2×C11312yescomplemented
287C2×#332C2×C11311yescharacteristic, complemented
288#1481C2×C11311yescharacteristic, complemented
289#1477C2×C11311yescharacteristic
290C113#1888511yescharacteristic, direct product factor, Sylow
291Q82—21no—
292#557C22×C11312yes—
293#554—21no—
294#554—22no—
295D4×Q8—22no—
296D4×Q8C22×C11312yes—
297#544—22no—
298#544—21no—
299#533—21no—
300#533C22×C11311yescharacteristic
301#533C22×C11311yescharacteristic
302C2×C4⋊Q8—21no—
303C2×C4⋊Q8C22×C11311yescharacteristic
304#520—21no—
305C4×#41C22×C11311yescharacteristic
306#500C22×C11312yes—
307#487C22×C11312yes—
308#484—22no—
309#479—21no—
310#478—21no—
311#477—22no—
312#477—21no—
313#477C22×C11311yescharacteristic
314#477C22×C11312yes—
315#476C22×C11311yescharacteristic
316#475C22×C11311yescharacteristic
317#474C22×C11311yescharacteristic
318#467—22no—
319#462—21no—
320#462C22×C11312yes—
321#431C22×C11311yescharacteristic
322#427—21no—
323C2×C4⋊C8C22×C11311yescharacteristic
324C2×C4⋊C8C22×C11311yescharacteristic
325#416—21no—
326#332C22×C11312yes—
327#332C22×C11312yes—
328Q8⋊C8C22×C11312yes—
329Q8⋊C8C22×C11312yes—
330Q8⋊C8C22×C11312yes—
331D4⋊C8C22×C11312yes—
332C2×#41D4×C11311yescharacteristic
333C22×Q8—22no—
334C22×Q8—21no—
335C2×Q16—22no—
336C22×C8—21no—
337C22×C8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—24no—
341C4⋊Q8—22no—
342C4⋊Q8—22no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8D4×C11311yescharacteristic
346C4⋊Q8D4×C11312yes—
347C4⋊Q8D4×C11311yescharacteristic
348C4⋊Q8C23×C11311yescharacteristic
349C4⋊Q8C23×C11311yescharacteristic
350C4⋊Q8C23×C11312yes—
351#125—22no—
352#125—24no—
353#125—22no—
354#125—21no—
355#125—21no—
356C22⋊Q8—22no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—21no—
360C22⋊Q8—22no—
361C22⋊Q8—24no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8D4×C11312yes—
365C4×Q8—22no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8D4×C11311yescharacteristic
372C4×Q8C23×C11311yescharacteristic
373C4×Q8C23×C11312yes—
374C4×D4—24no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4D4×C11311yescharacteristic
379C4×D4C23×C11311yescharacteristic
380#117—22no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117D4×C11311yescharacteristic
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4D4×C11312yes—
389C2×C42—21no—
390C2×C42C23×C11311yescharacteristic
391#107—21no—
392#107—21no—
393#107—22no—
394#107—24no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C11312yes—
401C4⋊C8C23×C11311yescharacteristic
402C4⋊C8C23×C11311yescharacteristic
403#103—21no—
404#103—21no—
405#103—22no—
406#103—22no—
407#103—24no—
408#102—21no—
409#102—21no—
410C22⋊C8—21no—
411C4×C8C23×C11312yes—
412#41—22no—
413#41Q16×C11314yescomplemented
414C2×Q8—24no—
415C2×Q8—21no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—81no—
421C2×Q8—81no—
422C2×Q8—82no—
423C2×Q8—82no—
424C2×Q8C2×D4×C11312yes—
425C2×Q8C2×D4×C11311yescharacteristic
426C2×D4—21no—
427C2×D4C2×D4×C11311yescharacteristic
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4C2×D4×C11311yescharacteristic
434C22×C4C2×D4×C11311yescharacteristic
435C22×C4C2×D4×C11311yescharacteristic
436Q16—82no—
437C2×C8—22no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—22no—
441C2×C8—42no—
442C2×C8—81no—
443C4⋊C4—24no—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—21no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—21no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C11314yes—
464C4⋊C4C2×D4×C11312yes—
465C4⋊C4C2×D4×C11311yescharacteristic
466C4⋊C4C2×D4×C11311yescharacteristic
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—41no—
473C42—24no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—22no—
478C42—41no—
479C42C2×D4×C11311yescharacteristic
480C42C2×D4×C11311yescharacteristic
481C42C2×D4×C11311yescharacteristic
482C42C24×C11311yescharacteristic
483C23—21no—
484C23#120×C11311yescharacteristic
485Q8—21no—
486Q8—22no—
487Q8—22no—
488Q8—42no—
489Q8—42no—
490Q8—42no—
491Q8—42no—
492Q8—41no—
493Q8—41no—
494Q8—82no—
495Q8—84no—
496Q8C2×Q16×C11312yes—
497D4—24no—
498D4—21no—
499D4C2×Q16×C11312yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—84no—
517C2×C4#120×C11311yescharacteristic
518C2×C4#120×C11311yescharacteristic
519C2×C4#120×C11311yescharacteristic
520C2×C4C2×Q16×C11312yes—
521C2×C4#137×C11312yes—
522C2×C4C22×D4×C11311yescharacteristic
523C2×C4C22×D4×C11311yescharacteristic
524C2×C4C22×D4×C11311yescharacteristic
525C8—42no—
526C8—41no—
527C8—41no—
528C8—42no—
529C22—21no—
530C22—21no—
531C22—22no—
532C22—41no—
533C22—41no—
534C22#451×C11312yes—
535C22C2×#120×C11311yescharacteristic
536C4—22no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—41no—
541C4—42no—
542C4—44no—
543C4—41no—
544C4—42no—
545C4—81no—
546C4—81no—
547C4#451×C11312yes—
548C4C22×Q16×C11311yescharacteristic
549C4C2×#137×C11311yescharacteristic
550C4#576×C11311yescharacteristic
551C4#577×C11311yescharacteristic
552C2—22no—
553C2—42no—
554C2C2×#451×C11311yescharacteristic
555C2C113×#301211yescharacteristic
556C2C113×#302011yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC42C24×C113
prime radicalC2×#41×C113D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C113×#3249C2semidirect
3. C113×#3230C2semidirect
5. C113×#1649C2semidirect
6. C113×#1648C2semidirect
7. C113×#1637C2semidirect
8. C113×#1636C2semidirect
9. C2×#332×C113C2semidirect
10. C113×#1481C2semidirect
134. #41×C113Q16semidirect
273. #18885C113direct (N × H)
280. #3249C2×C113semidirect
281. #3230C2×C113semidirect
283. #1649C2×C113semidirect
284. #1648C2×C113semidirect
285. #1637C2×C113semidirect
286. #1636C2×C113semidirect
287. C2×#332C2×C113semidirect
288. #1481C2×C113semidirect
290. C113#18885direct (N × H)
413. #41Q16×C113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C113×#35032
C113×#32492
C113×#32302
C113×#30762
C113×#16492
C113×#16482
C113×#16372
C113×#16362
C2×#332×C1132
C113×#14812
C113×#14772
#18885113